Rob said it right - just behind, without touching the fret.
Jessica - are you having this problem on a Stick? Or on a Dulcimer like the one in your avatar photo? If it's on a dulcimer, you may not have a wide enough stance with your legs, and the dulcimer is sagging a tiny bit as you push down at the first fret. When you're sitting you want a wide knee position, with your left knee under the first fret. Not knees together with the dulcimer teeter-totter-ing atop them.
Rich -- Since it's a "sometimes" thing, chances are your problem is "pilot error" rather than anything wrong with the instrument. Probably related to the way your left hand has to twist to get to that first fret on the melody string. Stick necks are much narrower than guitar/mando/uke necks and that requires your hand to bend differently. You could test this by laying the stick flat on a table and fretting while you can see what you're doing.
johnp is right too. The stick instrument, or as I call them American Citterns, isn't a dulcimer. By definition a dulcimer has no neck beyond the body. The folks here who play sticks may not look in General dulcimer discussions. If it's specific to sticks, you might want to post a question to the Stick Group.

Two of the pegs are not too bad but one of them when you get it tuned and bump it or touch it it jumps back again. I've used peg drops like Strumlelia recommended and it helps except for that one peg. I've tuned it down to CGG as DAA was too hard to tune and keep tuned. I use it when I want to play songs in DAA
